%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO040^1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:53:13 AM UTC 2026
% Result : Unsatisfiable 1.65s 1.46s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 82 ( 4 unt; 0 typ; 9 def)
% Number of atoms : 458 ( 70 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 375 ( 135 ~; 157 |; 0 &; 74 @)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $o > $o ).
thf(func_def_1,type,
h: $o > $i ).
thf(func_def_7,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f174,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f15,f24,f58,f59,f64,f68,f72,f75,f85,f88,f96,f103,f131,f152,f173]) ).
thf(f173,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f172]) ).
thf(f172,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f171]) ).
thf(f171,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f63,f157]) ).
thf(f157,plain,
( ( ( f @ $true )
= $false )
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f19,f51]) ).
thf(f51,plain,
( ( x = $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl0_7
<=> ( x = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f19,plain,
( ( ( f @ x )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl0_3
<=> ( ( f @ x )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f63,plain,
( ( ( f @ $true )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl0_9
<=> ( ( f @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f152,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f151]) ).
thf(f151,plain,
( $false
| ~ spl0_1
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ( $true = $false )
| ~ spl0_1
| spl0_3
| ~ spl0_4
| spl0_5
| spl0_7 ),
inference(forward_demodulation,[status(thm)],[f149,f132]) ).
thf(f132,plain,
( ( ( f @ $true )
= $false )
| ~ spl0_1
| spl0_3
| ~ spl0_4
| spl0_5 ),
inference(subsumption_resolution,[status(thm)],[f128,f42]) ).
thf(f42,plain,
( ( x != $false )
| spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl0_5
<=> ( x = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f128,plain,
( ( x = $false )
| ( ( f @ $true )
= $false )
| ~ spl0_1
| spl0_3
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f126]) ).
thf(f126,plain,
( ( x
!= ( f @ $true ) )
| ~ spl0_1
| spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
( ( x
!= ( f @ $true ) )
| ( $false != $false )
| ~ spl0_1
| spl0_3
| ~ spl0_4 ),
inference(constrained_superposition,[status(thm)],[f18,f92]) ).
thf(f92,plain,
( ( $false
= ( f @ ( f @ $true ) ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f23,f10]) ).
thf(f10,plain,
( ( ( f @ x )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f8]) ).
thf(f8,definition,
( spl0_1
<=> ( ( f @ x )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f23,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl0_4
<=> ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f18,plain,
( ( ( f @ x )
!= $false )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f149,plain,
( ( ( f @ $true )
= $true )
| ~ spl0_1
| ~ spl0_4
| spl0_7 ),
inference(subsumption_resolution,[status(thm)],[f118,f50]) ).
thf(f50,plain,
( ( x != $true )
| spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f118,plain,
( ( x = $true )
| ( ( f @ $true )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
( ( x
!= ( f @ $true ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $true = $false )
| ( x
!= ( f @ $true ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(constrained_superposition,[status(thm)],[f10,f92]) ).
thf(f131,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_4
| spl0_7
| spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f130]) ).
thf(f130,plain,
( $false
| ~ spl0_1
| spl0_3
| ~ spl0_4
| spl0_7
| spl0_9 ),
inference(subsumption_resolution,[status(thm)],[f129,f62]) ).
thf(f62,plain,
( ( ( f @ $true )
!= $true )
| spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f129,plain,
( ( ( f @ $true )
= $true )
| ~ spl0_1
| spl0_3
| ~ spl0_4
| spl0_7 ),
inference(subsumption_resolution,[status(thm)],[f127,f50]) ).
thf(f127,plain,
( ( x = $true )
| ( ( f @ $true )
= $true )
| ~ spl0_1
| spl0_3
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f126]) ).
thf(f103,plain,
( ~ spl0_7
| ~ spl0_1
| spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f102,f61,f8,f49]) ).
thf(f102,plain,
( ( x != $true )
| ~ spl0_1
| spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ( x != $true )
| ( $true != $true )
| ~ spl0_1
| spl0_9 ),
inference(constrained_superposition,[status(thm)],[f62,f10]) ).
thf(f96,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f95]) ).
thf(f95,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f63,f93]) ).
thf(f93,plain,
( ( ( f @ $true )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f92,f63]) ).
thf(f88,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f87]) ).
thf(f87,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f14,f23]) ).
thf(f14,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f12]) ).
thf(f12,definition,
( spl0_2
<=> ( ( f @ ( f @ ( f @ x ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f85,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f84]) ).
thf(f84,plain,
( $false
| ~ spl0_6
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $true = $false )
| ~ spl0_6
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f46,f56]) ).
thf(f56,plain,
( ( ( f @ $false )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f54,definition,
( spl0_8
<=> ( ( f @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f46,plain,
( ( $true
= ( f @ $false ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl0_6
<=> ( $true
= ( f @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f75,plain,
( ~ spl0_6
| spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f74,f40,f8,f44]) ).
thf(f74,plain,
( ( $true
!= ( f @ $false ) )
| spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f9,f41]) ).
thf(f41,plain,
( ( x = $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f9,plain,
( ( ( f @ x )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f8]) ).
thf(f72,plain,
( ~ spl0_3
| ~ spl0_5
| spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f71]) ).
thf(f71,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f70,f55]) ).
thf(f55,plain,
( ( ( f @ $false )
!= $false )
| spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f70,plain,
( ( ( f @ $false )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f19,f41]) ).
thf(f68,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f67]) ).
thf(f67,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f10,f19]) ).
thf(f64,plain,
( ~ spl0_8
| spl0_9
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f29,f17,f12,f61,f54]) ).
thf(f29,plain,
( ( ( f @ $false )
!= $false )
| ( ( f @ $true )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f27,f27]) ).
thf(f27,plain,
( ( $true
= ( f @ ( f @ $false ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f14,f19]) ).
thf(f59,plain,
( spl0_5
| spl0_8
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f35,f17,f12,f54,f40]) ).
thf(f35,plain,
( ( x = $false )
| ( ( f @ $false )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( x
!= ( f @ $false ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( x
!= ( f @ $false ) )
| ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f19,f27]) ).
thf(f58,plain,
( spl0_6
| spl0_7
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f34,f17,f12,f49,f44]) ).
thf(f34,plain,
( ( $true
= ( f @ $false ) )
| ( x = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f24,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f6,f21,f17]) ).
thf(f6,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f4]) ).
thf(f4,plain,
( ( f @ x )
!= ( f @ ( f @ ( f @ x ) ) ) ),
inference(equality_resolution,[status(thm)],[f3]) ).
thf(f3,plain,
( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
!= ( h @ ( f @ x ) ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
!= ( h @ ( f @ x ) ) ),
file('/export/starexec/sandbox/tmp/tmp.N2LNyHul8d/DTF2THF_14981.p',2) ).
thf(f15,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f5,f12,f8]) ).
thf(f5,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO040^1 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n020.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:22:27 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.48 ---- Original DTF file ---
% 0.19/0.48 thf(spec,logic,$$dhol).
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : SYO040^1 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.48 % Domain : Syntactic
% 0.19/0.48 % Problem : Unsatisfiable basic formula 2
% 0.19/0.48 % Version : Especial.
% 0.19/0.48 % English :
% 0.19/0.48
% 0.19/0.48 % Refs : [BS09a] Brown E. & Smolka (2009), Terminating Tableaux for the
% 0.19/0.48 % : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% 0.19/0.48 % Source : [BS09a]
% 0.19/0.48 % Names :
% 0.19/0.48
% 0.19/0.48 % Status : Unsatisfiable
% 0.19/0.48 % Rating : 0.00 v6.0.0, 0.33 v5.3.0, 0.67 v5.0.0, 0.33 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.19/0.48 % Syntax : Number of formulae : 4 ( 1 unt; 3 typ; 0 def)
% 0.19/0.48 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 1 ( 7 avg)
% 0.19/0.48 % Number of connectives : 7 ( 1 ~; 0 |; 0 &; 6 @)
% 0.19/0.48 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 2 ( 2 avg)
% 0.19/0.48 % Number of types : 2 ( 0 usr)
% 0.19/0.48 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.48 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.19/0.48 % SPC : TH0_UNS_EQU_NAR
% 0.19/0.48
% 0.19/0.48 % Comments : The fragment of simple type theory that restricts equations to
% 0.19/0.48 % base types and disallows lambda abstraction and quantification is
% 0.19/0.48 % decidable. This is an example.
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(f,type,
% 0.19/0.48 f: $o > $o ).
% 0.19/0.48
% 0.19/0.48 thf(h,type,
% 0.19/0.48 h: $o > $i ).
% 0.19/0.48
% 0.19/0.48 thf(x,type,
% 0.19/0.48 x: $o ).
% 0.19/0.48
% 0.19/0.48 thf(2,axiom,
% 0.19/0.48 ( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
% 0.19/0.48 != ( h @ ( f @ x ) ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------------------------
% 1.65/1.43 ---- Embedded in THF ---
% 1.65/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.43 %%% Generated on Tue Feb 24 14:22:28 EST 2026
% 1.65/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.43 %%% Logic specification used:
% 1.65/1.43 %%% thf(spec, logic, $$dhol).
% 1.65/1.43
% 1.65/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.N2LNyHul8d/DTF2DTF14981.p
% See solution above
% 1.65/1.43 ------------------------
% 1.65/1.44 ---- Cleaned THF ---
% 1.65/1.44 thf(f,type,
% 1.65/1.44 f: $o > $o ).
% 1.65/1.44
% 1.65/1.44 thf(h,type,
% 1.65/1.44 h: $o > $i ).
% 1.65/1.44
% 1.65/1.44 thf(x,type,
% 1.65/1.44 x: $o ).
% 1.65/1.44
% 1.65/1.44 thf(2,axiom,
% 1.65/1.44 ( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
% 1.65/1.44 != ( h @ ( f @ x ) ) ) ).
% 1.65/1.44 ------------------------
% 1.65/1.46 % (15091)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14981 for (3000ds/183Mi)
% 1.65/1.46 % (15095)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_14981 for (3000ds/2Mi)
% 1.65/1.46 % (15096)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_14981 for (3000ds/275Mi)
% 1.65/1.46 % (15093)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_14981 for (3000ds/27Mi)
% 1.65/1.46 % (15092)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_14981 for (3000ds/4Mi)
% 1.65/1.46 % (15094)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14981 for (3000ds/2Mi)
% 1.65/1.46 % (15097)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14981 for (3000ds/18Mi)
% 1.65/1.46 % (15096)Refutation not found, incomplete strategy
% 1.65/1.46 % (15096)------------------------------
% 1.65/1.46 % (15096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (15096)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.46
% 1.65/1.46
% 1.65/1.46 % (15096)Memory used [KB]: 5373
% 1.65/1.46 % (15096)Time elapsed: 0.002 s
% 1.65/1.46 % (15096)Instructions burned: 1 (million)
% 1.65/1.46 % (15096)------------------------------
% 1.65/1.46 % (15096)------------------------------
% 1.65/1.46 % (15095)Refutation not found, incomplete strategy
% 1.65/1.46 % (15095)------------------------------
% 1.65/1.46 % (15095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (15095)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.46
% 1.65/1.46
% 1.65/1.46 % (15095)Memory used [KB]: 5373
% 1.65/1.46 % (15095)Time elapsed: 0.003 s
% 1.65/1.46 % (15095)------------------------------
% 1.65/1.46 % (15095)------------------------------
% 1.65/1.46 % (15094)Refutation not found, incomplete strategy
% 1.65/1.46 % (15094)------------------------------
% 1.65/1.46 % (15094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (15093)Refutation not found, incomplete strategy
% 1.65/1.46 % (15093)------------------------------
% 1.65/1.46 % (15093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (15094)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.46
% 1.65/1.46
% 1.65/1.46 % (15094)Memory used [KB]: 5373
% 1.65/1.46 % (15094)Time elapsed: 0.003 s
% 1.65/1.46 % (15094)Instructions burned: 1 (million)
% 1.65/1.46 % (15094)------------------------------
% 1.65/1.46 % (15094)------------------------------
% 1.65/1.46 % (15093)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.46
% 1.65/1.46
% 1.65/1.46 % (15093)Memory used [KB]: 5373
% 1.65/1.46 % (15093)Time elapsed: 0.003 s
% 1.65/1.46 % (15093)Instructions burned: 1 (million)
% 1.65/1.46 % (15093)------------------------------
% 1.65/1.46 % (15093)------------------------------
% 1.65/1.46 % (15092)Instruction limit reached!
% 1.65/1.46 % (15092)------------------------------
% 1.65/1.46 % (15092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (15092)Termination reason: Unknown
% 1.65/1.46 % (15092)Termination phase: Saturation
% 1.65/1.46
% 1.65/1.46 % (15092)Memory used [KB]: 5500
% 1.65/1.46 % (15092)Time elapsed: 0.005 s
% 1.65/1.46 % (15092)Instructions burned: 4 (million)
% 1.65/1.46 % (15092)------------------------------
% 1.65/1.46 % (15092)------------------------------
% 1.65/1.46 % (15097)First to succeed.
% 1.65/1.46 % (15097)Refutation found. Thanks to Tanya!
% 1.65/1.46 % SZS status Unsatisfiable for DTF2THF_14981
% 1.65/1.46 % SZS output start Proof for DTF2THF_14981
% 1.65/1.46 thf(func_def_0, type, f: $o > $o).
% 1.65/1.46 thf(func_def_1, type, h: $o > $i).
% 1.65/1.46 thf(func_def_7, type, ph1: !>[X0: $tType]:(X0)).
% 1.65/1.46 thf(f174,plain,(
% 1.65/1.46 $false),
% 1.65/1.46 inference(avatar_sat_refutation,[status(thm)],[f15,f24,f58,f59,f64,f68,f72,f75,f85,f88,f96,f103,f131,f152,f173])).
% 1.65/1.46 thf(f173,plain,(
% 1.65/1.46 ~spl0_3 | ~spl0_7 | ~spl0_9),
% 1.65/1.46 inference(avatar_contradiction_clause,[status(thm)],[f172])).
% 1.65/1.46 thf(f172,plain,(
% 1.65/1.46 $false | (~spl0_3 | ~spl0_7 | ~spl0_9)),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f171])).
% 1.65/1.46 thf(f171,plain,(
% 1.65/1.46 ($true = $false) | (~spl0_3 | ~spl0_7 | ~spl0_9)),
% 1.65/1.46 inference(forward_demodulation,[status(thm)],[f63,f157])).
% 1.65/1.46 thf(f157,plain,(
% 1.65/1.46 ((f @ $true) = $false) | (~spl0_3 | ~spl0_7)),
% 1.65/1.46 inference(forward_demodulation,[status(thm)],[f19,f51])).
% 1.65/1.46 thf(f51,plain,(
% 1.65/1.46 (x = $true) | ~spl0_7),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.65/1.46 thf(f49,definition,(
% 1.65/1.46 spl0_7 <=> (x = $true)),
% 1.65/1.46 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.65/1.46 thf(f19,plain,(
% 1.65/1.46 ((f @ x) = $false) | ~spl0_3),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.65/1.46 thf(f17,definition,(
% 1.65/1.46 spl0_3 <=> ((f @ x) = $false)),
% 1.65/1.46 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.65/1.46 thf(f63,plain,(
% 1.65/1.46 ((f @ $true) = $true) | ~spl0_9),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.65/1.46 thf(f61,definition,(
% 1.65/1.46 spl0_9 <=> ((f @ $true) = $true)),
% 1.65/1.46 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.65/1.46 thf(f152,plain,(
% 1.65/1.46 ~spl0_1 | spl0_3 | ~spl0_4 | spl0_5 | spl0_7),
% 1.65/1.46 inference(avatar_contradiction_clause,[status(thm)],[f151])).
% 1.65/1.46 thf(f151,plain,(
% 1.65/1.46 $false | (~spl0_1 | spl0_3 | ~spl0_4 | spl0_5 | spl0_7)),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.65/1.46 thf(f150,plain,(
% 1.65/1.46 ($true = $false) | (~spl0_1 | spl0_3 | ~spl0_4 | spl0_5 | spl0_7)),
% 1.65/1.46 inference(forward_demodulation,[status(thm)],[f149,f132])).
% 1.65/1.46 thf(f132,plain,(
% 1.65/1.46 ((f @ $true) = $false) | (~spl0_1 | spl0_3 | ~spl0_4 | spl0_5)),
% 1.65/1.46 inference(subsumption_resolution,[status(thm)],[f128,f42])).
% 1.65/1.46 thf(f42,plain,(
% 1.65/1.46 (x != $false) | spl0_5),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.65/1.46 thf(f40,definition,(
% 1.65/1.46 spl0_5 <=> (x = $false)),
% 1.65/1.46 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.65/1.46 thf(f128,plain,(
% 1.65/1.46 (x = $false) | ((f @ $true) = $false) | (~spl0_1 | spl0_3 | ~spl0_4)),
% 1.65/1.46 inference(binary_proxy_clausification,[status(thm)],[f126])).
% 1.65/1.46 thf(f126,plain,(
% 1.65/1.46 (x != (f @ $true)) | (~spl0_1 | spl0_3 | ~spl0_4)),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.65/1.46 thf(f113,plain,(
% 1.65/1.46 (x != (f @ $true)) | ($false != $false) | (~spl0_1 | spl0_3 | ~spl0_4)),
% 1.65/1.46 inference(constrained_superposition,[status(thm)],[f18,f92])).
% 1.65/1.46 thf(f92,plain,(
% 1.65/1.46 ($false = (f @ (f @ $true))) | (~spl0_1 | ~spl0_4)),
% 1.65/1.46 inference(backward_demodulation,[status(thm)],[f23,f10])).
% 1.65/1.46 thf(f10,plain,(
% 1.65/1.46 ((f @ x) = $true) | ~spl0_1),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f8])).
% 1.65/1.46 thf(f8,definition,(
% 1.65/1.46 spl0_1 <=> ((f @ x) = $true)),
% 1.65/1.46 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.65/1.46 thf(f23,plain,(
% 1.65/1.46 ((f @ (f @ (f @ x))) = $false) | ~spl0_4),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.65/1.46 thf(f21,definition,(
% 1.65/1.46 spl0_4 <=> ((f @ (f @ (f @ x))) = $false)),
% 1.65/1.46 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.65/1.46 thf(f18,plain,(
% 1.65/1.46 ((f @ x) != $false) | spl0_3),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.65/1.46 thf(f149,plain,(
% 1.65/1.46 ((f @ $true) = $true) | (~spl0_1 | ~spl0_4 | spl0_7)),
% 1.65/1.46 inference(subsumption_resolution,[status(thm)],[f118,f50])).
% 1.65/1.46 thf(f50,plain,(
% 1.65/1.46 (x != $true) | spl0_7),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.65/1.46 thf(f118,plain,(
% 1.65/1.46 (x = $true) | ((f @ $true) = $true) | (~spl0_1 | ~spl0_4)),
% 1.65/1.46 inference(binary_proxy_clausification,[status(thm)],[f117])).
% 1.65/1.46 thf(f117,plain,(
% 1.65/1.46 (x != (f @ $true)) | (~spl0_1 | ~spl0_4)),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.65/1.46 thf(f112,plain,(
% 1.65/1.46 ($true = $false) | (x != (f @ $true)) | (~spl0_1 | ~spl0_4)),
% 1.65/1.46 inference(constrained_superposition,[status(thm)],[f10,f92])).
% 1.65/1.46 thf(f131,plain,(
% 1.65/1.46 ~spl0_1 | spl0_3 | ~spl0_4 | spl0_7 | spl0_9),
% 1.65/1.46 inference(avatar_contradiction_clause,[status(thm)],[f130])).
% 1.65/1.46 thf(f130,plain,(
% 1.65/1.46 $false | (~spl0_1 | spl0_3 | ~spl0_4 | spl0_7 | spl0_9)),
% 1.65/1.46 inference(subsumption_resolution,[status(thm)],[f129,f62])).
% 1.65/1.46 thf(f62,plain,(
% 1.65/1.46 ((f @ $true) != $true) | spl0_9),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.65/1.46 thf(f129,plain,(
% 1.65/1.46 ((f @ $true) = $true) | (~spl0_1 | spl0_3 | ~spl0_4 | spl0_7)),
% 1.65/1.46 inference(subsumption_resolution,[status(thm)],[f127,f50])).
% 1.65/1.46 thf(f127,plain,(
% 1.65/1.46 (x = $true) | ((f @ $true) = $true) | (~spl0_1 | spl0_3 | ~spl0_4)),
% 1.65/1.46 inference(binary_proxy_clausification,[status(thm)],[f126])).
% 1.65/1.46 thf(f103,plain,(
% 1.65/1.46 ~spl0_7 | ~spl0_1 | spl0_9),
% 1.65/1.46 inference(avatar_split_clause,[status(thm)],[f102,f61,f8,f49])).
% 1.65/1.46 thf(f102,plain,(
% 1.65/1.46 (x != $true) | (~spl0_1 | spl0_9)),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.65/1.46 thf(f100,plain,(
% 1.65/1.46 (x != $true) | ($true != $true) | (~spl0_1 | spl0_9)),
% 1.65/1.46 inference(constrained_superposition,[status(thm)],[f62,f10])).
% 1.65/1.46 thf(f96,plain,(
% 1.65/1.46 ~spl0_1 | ~spl0_4 | ~spl0_9),
% 1.65/1.46 inference(avatar_contradiction_clause,[status(thm)],[f95])).
% 1.65/1.46 thf(f95,plain,(
% 1.65/1.46 $false | (~spl0_1 | ~spl0_4 | ~spl0_9)),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.65/1.46 thf(f94,plain,(
% 1.65/1.46 ($true = $false) | (~spl0_1 | ~spl0_4 | ~spl0_9)),
% 1.65/1.46 inference(backward_demodulation,[status(thm)],[f63,f93])).
% 1.65/1.46 thf(f93,plain,(
% 1.65/1.46 ((f @ $true) = $false) | (~spl0_1 | ~spl0_4 | ~spl0_9)),
% 1.65/1.46 inference(forward_demodulation,[status(thm)],[f92,f63])).
% 1.65/1.46 thf(f88,plain,(
% 1.65/1.46 ~spl0_2 | ~spl0_4),
% 1.65/1.46 inference(avatar_contradiction_clause,[status(thm)],[f87])).
% 1.65/1.46 thf(f87,plain,(
% 1.65/1.46 $false | (~spl0_2 | ~spl0_4)),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.65/1.46 thf(f86,plain,(
% 1.65/1.46 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 1.65/1.46 inference(backward_demodulation,[status(thm)],[f14,f23])).
% 1.65/1.46 thf(f14,plain,(
% 1.65/1.46 ((f @ (f @ (f @ x))) = $true) | ~spl0_2),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f12])).
% 1.65/1.46 thf(f12,definition,(
% 1.65/1.46 spl0_2 <=> ((f @ (f @ (f @ x))) = $true)),
% 1.65/1.46 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.65/1.46 thf(f85,plain,(
% 1.65/1.46 ~spl0_6 | ~spl0_8),
% 1.65/1.46 inference(avatar_contradiction_clause,[status(thm)],[f84])).
% 1.65/1.46 thf(f84,plain,(
% 1.65/1.46 $false | (~spl0_6 | ~spl0_8)),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.65/1.46 thf(f83,plain,(
% 1.65/1.46 ($true = $false) | (~spl0_6 | ~spl0_8)),
% 1.65/1.46 inference(backward_demodulation,[status(thm)],[f46,f56])).
% 1.65/1.46 thf(f56,plain,(
% 1.65/1.46 ((f @ $false) = $false) | ~spl0_8),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.65/1.46 thf(f54,definition,(
% 1.65/1.46 spl0_8 <=> ((f @ $false) = $false)),
% 1.65/1.46 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.65/1.46 thf(f46,plain,(
% 1.65/1.46 ($true = (f @ $false)) | ~spl0_6),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.65/1.46 thf(f44,definition,(
% 1.65/1.46 spl0_6 <=> ($true = (f @ $false))),
% 1.65/1.46 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.65/1.46 thf(f75,plain,(
% 1.65/1.46 ~spl0_6 | spl0_1 | ~spl0_5),
% 1.65/1.46 inference(avatar_split_clause,[status(thm)],[f74,f40,f8,f44])).
% 1.65/1.46 thf(f74,plain,(
% 1.65/1.46 ($true != (f @ $false)) | (spl0_1 | ~spl0_5)),
% 1.65/1.46 inference(forward_demodulation,[status(thm)],[f9,f41])).
% 1.65/1.46 thf(f41,plain,(
% 1.65/1.46 (x = $false) | ~spl0_5),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.65/1.46 thf(f9,plain,(
% 1.65/1.46 ((f @ x) != $true) | spl0_1),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f8])).
% 1.65/1.46 thf(f72,plain,(
% 1.65/1.46 ~spl0_3 | ~spl0_5 | spl0_8),
% 1.65/1.46 inference(avatar_contradiction_clause,[status(thm)],[f71])).
% 1.65/1.46 thf(f71,plain,(
% 1.65/1.46 $false | (~spl0_3 | ~spl0_5 | spl0_8)),
% 1.65/1.46 inference(subsumption_resolution,[status(thm)],[f70,f55])).
% 1.65/1.46 thf(f55,plain,(
% 1.65/1.46 ((f @ $false) != $false) | spl0_8),
% 1.65/1.46 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.65/1.46 thf(f70,plain,(
% 1.65/1.46 ((f @ $false) = $false) | (~spl0_3 | ~spl0_5)),
% 1.65/1.46 inference(backward_demodulation,[status(thm)],[f19,f41])).
% 1.65/1.46 thf(f68,plain,(
% 1.65/1.46 ~spl0_1 | ~spl0_3),
% 1.65/1.46 inference(avatar_contradiction_clause,[status(thm)],[f67])).
% 1.65/1.46 thf(f67,plain,(
% 1.65/1.46 $false | (~spl0_1 | ~spl0_3)),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.65/1.46 thf(f66,plain,(
% 1.65/1.46 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 1.65/1.46 inference(forward_demodulation,[status(thm)],[f10,f19])).
% 1.65/1.46 thf(f64,plain,(
% 1.65/1.46 ~spl0_8 | spl0_9 | ~spl0_2 | ~spl0_3),
% 1.65/1.46 inference(avatar_split_clause,[status(thm)],[f29,f17,f12,f61,f54])).
% 1.65/1.46 thf(f29,plain,(
% 1.65/1.46 ((f @ $false) != $false) | ((f @ $true) = $true) | (~spl0_2 | ~spl0_3)),
% 1.65/1.46 inference(constrained_superposition,[status(thm)],[f27,f27])).
% 1.65/1.46 thf(f27,plain,(
% 1.65/1.46 ($true = (f @ (f @ $false))) | (~spl0_2 | ~spl0_3)),
% 1.65/1.46 inference(backward_demodulation,[status(thm)],[f14,f19])).
% 1.65/1.46 thf(f59,plain,(
% 1.65/1.46 spl0_5 | spl0_8 | ~spl0_2 | ~spl0_3),
% 1.65/1.46 inference(avatar_split_clause,[status(thm)],[f35,f17,f12,f54,f40])).
% 1.65/1.46 thf(f35,plain,(
% 1.65/1.46 (x = $false) | ((f @ $false) = $false) | (~spl0_2 | ~spl0_3)),
% 1.65/1.46 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.65/1.46 thf(f33,plain,(
% 1.65/1.46 (x != (f @ $false)) | (~spl0_2 | ~spl0_3)),
% 1.65/1.46 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.65/1.46 thf(f32,plain,(
% 1.65/1.46 (x != (f @ $false)) | ($true = $false) | (~spl0_2 | ~spl0_3)),
% 1.65/1.46 inference(constrained_superposition,[status(thm)],[f19,f27])).
% 1.65/1.46 thf(f58,plain,(
% 1.65/1.46 spl0_6 | spl0_7 | ~spl0_2 | ~spl0_3),
% 1.65/1.46 inference(avatar_split_clause,[status(thm)],[f34,f17,f12,f49,f44])).
% 1.65/1.46 thf(f34,plain,(
% 1.65/1.46 ($true = (f @ $false)) | (x = $true) | (~spl0_2 | ~spl0_3)),
% 1.65/1.46 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.65/1.46 thf(f24,plain,(
% 1.65/1.46 spl0_3 | spl0_4),
% 1.65/1.46 inference(avatar_split_clause,[status(thm)],[f6,f21,f17])).
% 1.65/1.46 thf(f6,plain,(
% 1.65/1.46 ((f @ (f @ (f @ x))) = $false) | ((f @ x) = $false)),
% 1.65/1.46 inference(binary_proxy_clausification,[status(thm)],[f4])).
% 1.65/1.46 thf(f4,plain,(
% 1.65/1.46 ((f @ x) != (f @ (f @ (f @ x))))),
% 1.65/1.46 inference(equality_resolution,[status(thm)],[f3])).
% 1.65/1.46 thf(f3,plain,(
% 1.65/1.46 ((h @ (f @ (f @ (f @ x)))) != (h @ (f @ x)))),
% 1.65/1.46 inference(cnf_transformation,[status(thm)],[f1])).
% 1.65/1.46 thf(f1,axiom,(
% 1.65/1.46 ((h @ (f @ (f @ (f @ x)))) != (h @ (f @ x)))),
% 1.65/1.46 file('/export/starexec/sandbox/tmp/tmp.N2LNyHul8d/DTF2THF_14981.p',2)).
% 1.65/1.47 thf(f15,plain,(
% 1.65/1.47 spl0_1 | spl0_2),
% 1.65/1.47 inference(avatar_split_clause,[status(thm)],[f5,f12,f8])).
% 1.65/1.47 thf(f5,plain,(
% 1.65/1.47 ((f @ (f @ (f @ x))) = $true) | ((f @ x) = $true)),
% 1.65/1.47 inference(binary_proxy_clausification,[status(thm)],[f4])).
% 1.65/1.47 % SZS output end Proof for DTF2THF_14981
% 1.65/1.47 % (15097)------------------------------
% 1.65/1.47 % (15097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.47 % (15097)Termination reason: Refutation
% 1.65/1.47
% 1.65/1.47 % (15097)Memory used [KB]: 5500
% 1.65/1.47 % (15097)Time elapsed: 0.009 s
% 1.65/1.47 % (15097)Instructions burned: 8 (million)
% 1.65/1.47 % (15097)------------------------------
% 1.65/1.47 % (15097)------------------------------
% 1.65/1.47 % (15090)Success in time 0.022 s
%------------------------------------------------------------------------------